It is known to mount the shaft of an open-end spinning rotor radially in the wedge-shaped gap formed by supporting disks and at the same time, to press it against the supporting disks by means of a tangential belt or a pressure roller (German Offenlegungsschrift 1,901,453). The supporting disks are provided with coverings consisting of damping material, for example, plastic, in order to guarantee quiet running of the spinning rotor rotating at high speeds and reduce the noise. During operation, the running surface is exposed, due to the shaft rotating at high speed and pressed against the running surface with the pressure required for the drive, to a considerable stress which is further intensified as a result of a prevailing balance and an axial thrust (German Offenlegungsschrift 2,112,913) generated via the supporting disks and exerted on the shaft. This stress results in relatively rapid wear and in the destruction of the running surface and consequently the rotor mounting. It is necessary to exchange the supporting disks, which, because of the plurality of spinning stations, each time entails considerable costs in terms of material, assembly and lost production time of the machine.